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Welcome to math!
Tuesday, March 27
Objective of Investigation 1.2
• Review properties of quadrilaterals
• Connect properties of figures to
coordinate representations
• Draw shapes on a coordinate grid
Fraction Problem of the day
• There are 24 hours in a day and scientists tell
us that we should sleep for 3/8 of the day.
How much time should we spend sleeping?
3/8 of 24 means 3/8 times 24!
Cross simplify when you multiply
• There are 24 hours in a day and scientists tell
us that we should sleep for 3/8 of the day.
How much time should we spend sleeping?
3 . 24
8 1
Reduce 8 and 24 by a factor of 8
• There are 24 hours in a day and scientists tell
us that we should sleep for 3/8 of the day.
How much time should we spend sleeping?
3 . 24 3
1 8 1
Multiply across numerator and
denominator
• There are 24 hours in a day and scientists tell
us that we should sleep for 3/8 of the day.
How much time should we spend sleeping?
3 . 24 3 = 9 hours
1 8 1
Euclid
• Nobody knows much about
Euclid's life anymore - it is
all forgotten. We only know
that he worked at the
University of Alexandria, in
Egypt, for a while. There are
no pictures of him. We can't
even be sure he existed;
Euclid could be a made-up
name for a committee of
mathematicians all working
together.
Euclid lived 2300 years ago
• Either way, Euclid (or the
people who called
themselves Euclid) must
have lived around 300 BC,
in the Hellenistic period.
He (or they) seems to
have studied at Plato's
Academy in Athens,
where he learned some
of the mathematics that
is in his books. He
probably knew Aristotle
there.
Use of Logic
• Like Anaxagoras before him,
Euclid wanted to prove that
things were true by using logic
and reason. We still have
copies of Euclid's books today,
and they begin with basic
definitions of a point and a
line and shapes, and then go
on to use geometry to prove,
for instance, that all right
angles are equal, that you can
draw a straight line between
any two points, and that two
things which are both equal to
the same thing are also equal
to each other.
Euclid’s famous book Elements
Euclid's later books
teach more
advanced math,
including how
triangles and circles
work, irrational
numbers, and threedimensional
geometry.
Euclid is considered…
the Father of Geometry
• Euclid is famous because
his books were so easy to
understand that they
were used as the main
math book in all schools
in Europe, West Asia, and
America for two thousand
years, until the 20th
century. There are still
mathematicians working
today who began
studying geometry from
Euclid's books.
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Things you should already know
A vertex is a where to line segments
meet to form a corner.
Vertices is the plural form for vertex
A vertex is a where to line segments
meet to form a corner.
What are the properties of different
quadrilaterals?
More quadrilateral properties
Right Triangle Properties
• Three sided figure
• One of the angles = 90°